Weak Factorizations of the Hardy space $H^1({\mathbb{R}}^n)$ in terms of Multilinear Riesz Transforms

Abstract

This paper provides a constructive proof of the weak factorizations of the classical Hardy space $H^1({\mathbb{R}}^n)$ in terms of multilinear Riesz transforms. As a direct application, we obtain a new proof of the characterization of $\mathrm{BMO}({\mathbb{R}}^n)$ (the dual of $H^1({\mathbb{R}}^n)$) via commutators of the multilinear Riesz transforms.

improved some typos

References in corpus (3)

• Characterizations of BMO through commutators of bilinear singular integral operators
• Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting
• Characterizations of $H_{{\Delta }_N}^1({\mathbb{R}}^n)$ and $\mathrm{BM}{\mathrm{O}}_{{\mathrm{\Delta }}_{\mathrm{N}}}({\mathbb{R}}^{\mathrm{n}})$ via Weak Factorizations and Commutators

Cited by in corpus (4)

• Boundedness and compactness characterizations of Cauchy integral commutators on Morrey spaces
• The unified theory for the necessity of bounded commutators and applications
• A note on commutator in the multilinear setting
• Weak factorization of the Hardy space $H^p$ for small values of $p$, in the multilinear setting